The non-destructive investigation of samples is an important objective in various technical fields like material sciences, non-destructive testing, medical examinations, archaeology, construction technique, techniques concerning security matters etc. One approach for obtaining an image of a sample e.g. by computer tomography is based on an irradiation through a sample plane from different projection directions with X-rays, followed by the reconstruction of the sample plane on the basis of attenuation data measured at different directions. The entirety of the measured attenuation data can be described in terms of so-called Radon data in a Radon space.
Different reconstruction methods for Radon data are known today. For an introduction to the mathematical and physical principles of conventional image reconstruction, reference is made to the textbooks “Computed Tomography—Fundamentals, System Technology, Image Quality, Applications” by W. A. Kalender (1st. edition, ISBN 3-89578-081-2); “Image Reconstruction from Projections: The Fundamentals of Computerized Tomography” by G. T. Herman, Academic Press, 1980; and “Einführung in die Computertomographie” by Thorsten M. Buzug (Springer-Verlag, Berlin 2004). The conventional reconstruction methods can be summarized as iterative reconstruction methods and filtered back-projection methods.
The iterative reconstruction is an approximation method based on a plurality of iteration steps. The essential disadvantage of the iterative reconstruction of higher resolution images is that the iteration leads to extremely long calculation times. The filtered back-projection method relies in principle on the Fourier-slice theorem describing a relationship between the Fourier transform of the Radon data and Fourier transformed image data. A general disadvantage of using the Fourier-slice theorem lies in the fact that an interpolation step in the reconstruction results in errors and artifacts which have a tendency to increase with increasing space frequency. This disadvantage can only be avoided by using detectors with high resolution. However, the application of these detectors is limited in terms of dose burden, costs and data processing time.
An improved method of reconstructing image functions from Radon data is described in EP 04031043.5 (unpublished on the filing date of the present patent specification). With this method of using orthogonal polynomial expansions on the disk (in the following: OPED algorithm), an image function representing the region of investigation is determined from Radon data as a sum of polynomials multiplied with values of projection functions measured corresponding to a plurality of predetermined projection directions through the region of investigation. The OPED algorithm has essential advantages in particular in terms of computational time reduction, noise reduction and improved imaging resolution.
Conventional computer tomography devices used for collecting Radon data comprise an X-ray source for irradiating the object, a detector device for measuring attenuated irradiation passing through the object and a holding device for holding the object. The holding device is arranged in a gantry, which comprises a carrier for a rotatable irradiation unit with the X-ray source and the detector device. With the so-called 4th generation of computer tomography devices, the rotatable source-detector-unit is replaced by a combination of a rotatable X-ray source 10′ with a fixed detector ring 20′ as illustrated in FIG. 13 (see the above text book “Einführung in die Computertomographie” by Thorsten M. Buzug, page 51). The detector ring 20′ includes about 5.000 detector elements arranged on a circle around the object. In order to avoid an irradiation through detectors near the X-ray source, the conventional technique includes a dynamic inclination of the detector ring 20′. The dynamic inclination represents a disadvantage as it requires a complex structure and inclination control of the detector ring.
The conventional computer tomography devices have a further disadvantage in that not all irradiation applied to the object is collected and transferred to useful reconstruction data. Therefore, the object, e.g. a patient is subjected to an unnecessary high irradiation dose.
The above disadvantages are associated not only with the conventional CT imaging, but also with all available reconstruction methods related to Radon data.